Problem: How many triangles are in the figure to the right? [asy]
defaultpen(linewidth(0.7));
pair hexcoords (real over, real upover)
{

return dir(0)*over+dir(60)*upover;
}
real r = 0.3;
int i,j;
for(i=0;i<=2;++i)

{

for(j=0;j<=2-i;++j)

{

draw(hexcoords(i,j)--hexcoords(i+1,j));

draw(hexcoords(i,j)--hexcoords(i,j+1));

draw(hexcoords(i+1,j)--hexcoords(i,j+1));

}

}
draw(hexcoords(1,2)--hexcoords(1,3)--hexcoords(-1,3)--hexcoords(0,2));[/asy]
There are 11 small triangles, 4 triangles which consist of four small triangles, and 1 triangle which consists of 9 small triangles.  In total, there are $\boxed{16}$ triangles.